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PH-EP-2015-098

(Submitted on 23 Apr 2015)

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Abstract

Angular correlations in $B^+\to X(3872) K^+$ decays, with $X(3872)\to \rho^0
J/\psi$, $\rho^0\to\pi^+\pi^-$ and $J/\psi \to\mu^+\mu^-$, are used to measure
orbital angular momentum contributions and to determine the $J^{PC}$ value of
the $X(3872)$ meson. The data correspond to an integrated luminosity of 3.0
fb$^{-1}$ of proton-proton collisions collected with the LHCb detector. This
determination, for the first time performed without assuming a value for the
orbital angular momentum, confirms the quantum numbers to be $J^{PC}=1^{++}$.
The $X(3872)$ is found to decay predominantly through S wave and an upper limit
of $4\%$ at $95\%$ C.L. is set on the fraction of D wave.

Distributions of the test statistic $t \equiv -2\ln[{\cal L}(J_X^{\rm alt}))/{\cal L}(1^{++})]$,
for the simulated experiments
under the $J^{PC}=J_X^{\rm alt}$ hypothesis
(blue solid histograms)
and under the $J^{PC}=1^{++}$ hypothesis (red dashed histograms).
The values of the test statistics for the data, $t_{\rm data}$,
are shown by the solid vertical lines.

Background-subtracted
distribution of $\cos\theta_X$ for
candidates with $|\cos\theta_{\rho}|>0.6$
for the data (points with error bars)
compared to the expected distributions
for various $X(3872)$ $J^{PC}$ assignments (solid histograms)
with the $B_{LS}$ amplitudes obtained by the
fit to the data in the five-dimensional angular space.
The fit displays are normalized to the observed number of
the signal events in the full angular phase space.

Tables and captions

Parity-allowed $LS$ couplings in the $X(3872)\rightarrow \rho^0 { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} $ decay.
For comparison, we also list a subset of these couplings corresponding to
the lowest $L$, used in the previous determinations [14,16,17]
of the $X(3872)$ quantum numbers.